Ian Kinsler’s two-run home run off Bryan Shaw in the seventh inning put the Tigers ahead for good.

The Tigers went on to complete a three-game sweep of the Indians with a 6-4 victory on Sunday at Comerica Park.

The Tigers (83-66) now lead the American League’s Central Division by 1½ games, after the Royals (81-67) lost, 8-4, to the Red Sox on Sunday.

“Every game is huge. It has been (like that) now for little over a week, probably,” said Tigers manager Brad Ausmus said. “We were able to work our way back into the fight, right into the thick of it, and now every game matters. Every game Kansas City (plays) matters.”

Kinsler sent a 3-1 pitch from Shaw over the wall in left-center. It was Kinsler’s 14th home run of the season. It was the second straight day that Shaw had given up a go-ahead home run against the Tigers.

Alex Avila homered off Shaw in the eighth inning on Saturday and the Tigers went on to win that game, 5-4.

“He’s been outstanding for them as a setup guy,” Ausmus said of Shaw. “Certainly I’m not upset that we got to him the last couple days. It doesn’t take anything away from the type of season he’s had.”

J.D. Martinez accounted for the first two runs for the Tigers. He hit a solo home run in the fourth and added an RBI single in the sixth.

The Tigers added a couple of insurance runs in the eighth. Don Kelly scored on a wild pitch from C.C. Lee during an intentional walk to Kinsler. Eugenio Suarez scored when Torii Hunter grounded into a force out to give the Tigers a 6-3 lead.

Joe Nathan gave up a leadoff single to Michael Brantley, an RBI double to right to Carlos Santana and a walk to Jason Kipnis with none out in the ninth. Nathan regrouped after getting visited by pitching coach Jeff Jones. Yan Gomes grounded into a double play, and pinch hitter Jason Giambi popped out to left to end the game.

“It wasn’t easy,” Nathan said. “I knew I was tired, I knew I was running on some fumes out there and didn’t feel so fresh. The meeting kind of gave me a little blow and more so let me collect my thoughts. From there, it was just grind out and try to get a win any way we could. I knew how big this win could be today, especially with Kansas City (losing). I knew we had a chance to gain some ground.”

Starter Justin Verlander allowed three runs on six hits and three walks over 52/3 innings with six strikeouts for the Tigers.

“His blister flared up a little bit again on him,” Ausmus said of Verlander. “I don’t think it’ll be an issue for him going forward. He did a nice job, gave us a chance to win.”

Verlander was in a bases-loaded jam with one out in the fourth inning before getting out of trouble unscathed. Lonnie Chisenhall popped out to second and Roberto Perez lined out to center.

The Tigers took a 1-0 lead in the bottom of the fourth on a home run of the season hit by J.D. Martinez. The ball disappeared into the shrubbery just above the wall in centerfield. It was his 22nd home run of the season.

“You don’t see many guys reach those bushes out there,” Ausmus said. “But we’ve known since we’ve called him up here, in terms of raw power, he’s up there with anyone in the Major Leagues. Certainly doesn’t shock me, but it was nice to see.”

The Indians came back to tie the game in the top of the fifth and scored two more runs in the sixth.

Michael Bourn scored on a sacrifice fly by Carlos Santana to tie the game in the fifth.

Verlander gave up a leadoff single to Yan Gomes in the sixth before striking out David Murphy and Lonnie Chisenhall. Verlander’s day ended after giving up a single to Perez.

Lefty Blaine Hardy came in to pitch to Michael Bourn and gave up a walk to load the bases. An infield single by Jose Ramirez broke a 1-1 tie. Hardy hit Michael Brantley with a pitch with the bases loaded to give the Indians a two-run lead. Evan Reed replaced Hardy and got Santana to ground out to second.

A fielding error by Santana in the sixth gave the Tigers hope for a comeback. After Miguel Cabrera singled, Victor Martinez hit a ball to first that slipped past the glove of Santana. J.D. Martinez followed with an RBI single, cutting the deficit to 3-2.

Kinsler’s heroics came an inning later.

The Tigers head to Minnesota to face the Twins, who are 20 games behind in the Central.

The race

AL Central

W-L

GB

DET

83-66

—

K.C.

81-67

1½

CLE

76-72

6½

CHI

68-81

15

MIN

63-86

20

Tripping up the Tribe

J.D. Martinez hit his seventh home run of the season against Cleveland. Only 8 other Tigers have hit seven or more against the Tribe in a single season: